- Open Access
Spin fluctuations steer the electronic behavior in the skutterudite
Phys. Rev. Research 8, 013174 – Published 17 February, 2026
DOI: https://doi.org/10.1103/lyy4-cmf6
Abstract
Skutterudites are promising materials for thermoelectric and spintronics applications. Here, we explore spin fluctuations in the skutterudite and their effect on its electronic structure using Hubbard-corrected density-functional theory calculations. We identify multiple magnetic- and charge-disproportionated configurations, with an antiferromagnetic metallic ground state. Paramagnetic fluctuations modeled through a special quasirandom spin structure open a 61 meV gap, consistent with experiments. This state features nondegenerate spin channels and band-avoided crossings, resembling a Luttinger-compensated ferrimagnet. Mapping the electronic structure to a Heisenberg Hamiltonian fails to explain the low Néel temperature (), suggesting that factors such as stoichiometry and magnetic exchange frustration may play an important role, calling for more detailed experimental investigations.
Physics Subject Headings (PhySH)
Article Text
References (99)
- I. Shirotani, T. Uchiumi, K. Ohno, C. Sekine, Y. Nakazawa, K. Kanoda, S. Todo, and T. Yagi, Superconductivity of filled skutterudites laru 4 as 12 and prru 4 as 12, Phys. Rev. B 56, 7866 (1997).
- M. B. Maple, P.-C. Ho, V. S. Zapf, N. A. Frederick, E. D. Bauer, W. M. Yuhasz, F. M. Woodward, and J. W. Lynn, Heavy fermion superconductivity in the filled skutterudite compound , J. Phys. Soc. Jpn. 71, 23 (2002).
- M. E. Danebrock, C. B. Evers, and W. Jeitschko, Magnetic properties of alkaline earth and lanthanoid iron antimonides () with the structure, J. Phys. Chem. Solids 57, 381 (1996).
- E. Bauer, S. Berger, C. Paul, M. D. Mea, G. Hilscher, H. Michor, M. Reissner, W. Steiner, A. Grytsiv, P. Rogl, et al., Crystal field effects and thermoelectric properties of skutterudite, Phys. Rev. B 66, 214421 (2002).
- E. Bauer, A. Slebarski, E. Freeman, C. Sirvent, and M. Maple, Kondo insulating behaviour in the filled skutterudite compound , J. Phys.: Condens. Matter 13, 4495 (2001).
- N. Takeda and M. Ishikawa, The effect of La substitution and magnetic field on non-Fermi-liquid behaviour in , J. Phys.: Condens. Matter 13, 5971 (2001).
- R. Baumbach, P. Ho, T. Sayles, M. Maple, R. Wawryk, T. Cichorek, A. Pietraszko, and Z. Henkie, Non-Fermi liquid behavior in the filled skutterudite compound , J. Phys.: Condens. Matter 20, 075110 (2008).
- C. Sekine, T. Uchiumi, I. Shirotani, and T. Yagi, Metal-insulator transition in with skutterudite structure, Phys. Rev. Lett. 79, 3218 (1997).
- N. R. Dilley, E. J. Freeman, E. D. Bauer, and M. B. Maple, Intermediate valence in the filled skutterudite compound , Phys. Rev. B 58, 6287 (1998).
- D. J. Singh and I. I. Mazin, Calculated thermoelectric properties of La-filled skutterudites, Phys. Rev. B 56, R1650 (1997).
- M. Yang and W.-M. Liu, The d-p band-inversion topological insulator in bismuth-based skutterudites, Sci. Rep. 4, 5131 (2014).
- P.-A. Zong, R. Hanus, M. Dylla, Y. Tang, J. Liao, Q. Zhang, G. J. Snyder, and L. Chen, Skutterudite with graphene-modified grain-boundary complexion enhances zt enabling high-efficiency thermoelectric device, Energy Environ. Sci. 10, 183 (2017).
- Q. Zhang, J. Liao, Y. Tang, M. Gu, C. Ming, P. Qiu, S. Bai, X. Shi, C. Uher, and L. Chen, Realizing a thermoelectric conversion efficiency of in bismuth telluride/skutterudite segmented modules through full-parameter optimization and energy-loss minimized integration, Energy Environ. Sci. 10, 956 (2017).
- B. C. Sales, Filled skutterudites, Handb. Phys. Chem. Rare Earths 33, 1 (2003).
- G. Nolas, G. Slack, D. Morelli, T. Tritt, and A. Ehrlich, The effect of rare-earth filling on the lattice thermal conductivity of skutterudites, J. Appl. Phys. 79, 4002 (1996).
- A. Leithe-Jasper, W. Schnelle, H. Rosner, N. Senthilkumaran, A. Rabis, M. Baenitz, A. Gippius, E. Morozova, J. A. Mydosh, and Y. Grin, Ferromagnetic ordering in alkali-metal iron antimonides: and , Phys. Rev. Lett. 91, 037208 (2003).
- P. Qiu, J. Yang, R. Liu, X. Shi, X. Huang, G. Snyder, W. Zhang, and L. Chen, Hightemperature electrical and thermal transport properties of fully filled skutterudites (R= Ca, Sr, Ba, La, Ce, Pr, Nd, Eu, and Yb), J. Appl. Phys. 109, 063713 (2011).
- L. Chaput, P. Pécheur, J. Tobola, and H. Scherrer, Transport in doped skutterudites: Ab initio electronic structure calculations, Phys. Rev. B 72, 085126 (2005).
- Y. Tang, Z. M. Gibbs, L. A. Agapito, G. Li, H.-S. Kim, M. B. Nardelli, S. Curtarolo, and G. J. Snyder, Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in skutterudites, Nat. Mater. 14, 1223 (2015).
- M. M. Koza, M. R. Johnson, R. Viennois, H. Mutka, L. Girard, and D. Ravot, Breakdown of phonon glass paradigm in La-and Ce-filled skutterudites, Nat. Mater. 7, 805 (2008).
- E. Di Lucente, M. Simoncelli, and N. Marzari, Crossover from Boltzmann to Wigner thermal transport in thermoelectric skutterudites, Phys. Rev. Res. 5, 033125 (2023).
- A. Möchel, I. Sergueev, N. Nguyen, G. J. Long, F. Grandjean, D. C. Johnson, and R. P. Hermann, Lattice dynamics in the skutterudite, Phys. Rev. B 84, 064302 (2011).
- G. A. Slack and V. G. Tsoukala, Some properties of semiconducting , J. Appl. Phys. 76, 1665 (1994).
- J. O. Sofo and G. D. Mahan, Electronic structure of : A narrow-band-gap semiconductor, Phys. Rev. B 58, 15620 (1998).
- E. Kurmaev, A. Moewes, I. Shein, L. Finkelstein, A. Ivanovskii, and H. Anno, Electronic structure and thermoelectric properties of skutterudite compounds, J. Phys.: Condens. Matter 16, 979 (2004).
- J. Yang, M. G. Endres, and G. P. Meisner, Valence of Cr in skutterudites: electrical transport and magnetic properties of Cr-doped , Phys. Rev. B 66, 014436 (2002).
- D. Wee, B. Kozinsky, N. Marzari, and M. Fornari, Effects of filling in : Local structure, band gap, and phonons from first principles, Phys. Rev. B 81, 045204 (2010).
- M. V. Daniel, L. Hammerschmidt, C. Schmidt, F. Timmermann, J. Franke, N. Jöhrmann, M. Hietschold, D. C. Johnson, B. Paulus, and M. Albrecht, Structural and thermoelectric properties of skutterudite thin films, Phys. Rev. B 91, 085410 (2015).
- P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
- W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
- H. J. Kulik, M. Cococcioni, D. A. Scherlis, and N. Marzari, Density functional theory in transition-metal chemistry: A self-consistent Hubbard u approach, Phys. Rev. Lett. 97, 103001 (2006).
- M. Cococcioni and N. Marzari, Energetics and cathode voltages of olivines (= Fe, Mn) from extended Hubbard functionals, Phys. Rev. Mater. 3, 033801 (2019).
- I. Timrov, F. Aquilante, M. Cococcioni, and N. Marzari, Accurate electronic properties and intercalation voltages of olivine-type Li-ion cathode materials from extended Hubbard functionals, PRX Energy 1, 033003 (2022).
- V. I. Anisimov, J. Zaanen, and O. K. Andersen, Band theory and mott insulators: Hubbard U instead of stoner I, Phys. Rev. B 44, 943 (1991).
- S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57, 1505 (1998).
- M. Cococcioni and S. de Gironcoli, Linear response approach to the calculation of the effective interaction parameters in the LDA+U method, Phys. Rev. B 71, 035105 (2005).
- I. Timrov, N. Marzari, and M. Cococcioni, Hubbard parameters from densityfunctional perturbation theory, Phys. Rev. B 98, 085127 (2018).
- I. Timrov, N. Marzari, and M. Cococcioni, Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations, Phys. Rev. B 103, 045141 (2021).
- A. Zunger, S.-H. Wei, L. G. Ferreira, and J. E. Bernard, Special quasirandom structures, Phys. Rev. Lett. 65, 353 (1990).
- O. I. Malyi and A. Zunger, False metals, real insulators, and degenerate gapped metals, Appl. Phys. Rev. 7, 041310 (2020).
- G. Trimarchi, Z. Wang, and A. Zunger, Polymorphous band structure model of gapping in the antiferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO, Phys. Rev. B 97, 035107 (2018).
- J. Varignon, M. Bibes, and A. Zunger, Origin of band gaps in 3d perovskite oxides, Nat. Commun. 10, 1658 (2019).
- Z. Wang, X.-G. Zhao, R. Koch, S. J. L. Billinge, and A. Zunger, Understanding electronic peculiarities in tetragonal FeSe as local structural symmetry breaking, Phys. Rev. B 102, 235121 (2020).
- S.-H. Wei, L. G. Ferreira, J. E. Bernard, and A. Zunger, Electronic properties of random alloys: Special quasirandom structures, Phys. Rev. B 42, 9622 (1990).
- G. Rey, A. Redinger, J. Sendler, T. P. Weiss, M. Thevenin, M. Guennou, B. El Adib, and S. Siebentritt, The band gap of : Effect of order-disorder, Appl. Phys. Lett. 105, 112106 (2014).
- C. González, J. Guo, J. Ortega, F. Flores, and H. H. Weitering, Mechanism of the band gap opening across the order-disorder transition of Si(111)(4×1)-In, Phys. Rev. Lett. 102, 115501 (2009).
- T. Veal, N. Feldberg, N. F. Quackenbush, W. M. Linhart, D. O. Scanlon, L. F. Piper, and S. M. Durbin, Band gap dependence on cation disorder in Solar absorber, Adv. Energy Mater. 5, 1501462 (2015).
- A. van de Walle, M. Asta, and G. Ceder, The alloy theoretic automated toolkit: A user guide, Calphad 26, 539 (2002).
- A. I. Liechtenstein, M. I. Katsnelson, V. P. Antropov, and V. A. Gubanov, Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys, J. Magn. Magn. Mater. 67, 65 (1987).
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, et al., Quantum espresso: a modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
- F. J. dos Santos, flavianojs/DFWannier.jl, GitHub (2024), https://github.com/flavianojs/DFWannier.jl.
- E. Şaşıoğlu, L. M. Sandratskii, P. Bruno, and I. Galanakis, Exchange interactions and temperature dependence of magnetization in half-metallic Heusler alloys, Phys. Rev. B 72, 184415 (2005).
- D. A. Garanin, Self-consistent Gaussian approximation for classical spin systems: Thermodynamics, Phys. Rev. B 53, 11593 (1996).
- R. F. L. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. A. Ellis, and R. W. Chantrell, Atomistic spin model simulations of magnetic nanomaterials, J. Phys.: Condens. Matter 26, 103202 (2014).
- VAMPIRE, version 6.0.0, https://vampire.york.ac.uk.
- L. A. Mariano, B. Vlaisavljevich, and R. Poloni, Biased spin-state energetics of Fe (ii) molecular complexes within density-functional theory and the linear-response Hubbard U correction, J. Chem. Theory Comput. 16, 6755 (2020).
- L. A. Mariano, B. Vlaisavljevich, and R. Poloni, Improved spin-state energy differences of Fe (ii) molecular and crystalline complexes via the Hubbard u-corrected density, J. Chem. Theory Comput. 17, 2807 (2021).
- L. Ponet, E. Di Lucente, and N. Marzari, The energy landscape of magnetic materials, npj Comput. Mater. 10, 151 (2024).
- H. J. Kulik and N. Marzari, A self-consistent Hubbard U density-functional theory approach to the addition-elimination reactions of hydrocarbons on bare FeO+, J. Chem. Phys. 129, 134314 (2008).
- H. Hsu, K. Umemoto, M. Cococcioni, and R. Wentzcovitch, First-principles study for low-spin with a structurally consistent Hubbard , Phys. Rev. B 79, 125124 (2009).
- H. Hsu, P. Blaha, M. Cococcioni, and R. M. Wentzcovitch, Spin-state crossover and hyperfine interactions of ferric iron in perovskite, Phys. Rev. Lett. 106, 118501 (2011).
- M. D. Hornbostel, E. J. Hyer, J. Thiel, and D. C. Johnson, Rational synthesis of metastable skutterudite compounds using multilayer precursors, J. Am. Chem. Soc. 119, 2665 (1997).
- M. Råsander, L. Bergqvist, and A. Delin, Electronic structure and lattice dynamics in the skutterudite from density functional theory, Phys. Rev. B 91, 014303 (2015).
- J. Kim, R. Ramesh, and N. Kioussis, Revealing the hidden structural phases of FeRh, Phys. Rev. B 94, 180407(R) (2016).
- S. Lemal, N. Nguyen, J. de Boor, P. Ghosez, J. Varignon, B. Klobes, R. P. Hermann, and M. J. Verstraete, Thermoelectric properties of the unfilled skutterudite from first principles and seebeck local probes, Phys. Rev. B 92, 205204 (2015).
- P. H.-L. Sit, R. Car, M. H. Cohen, and A. Selloni, Simple, unambiguous theoretical approach to oxidation state determination via first-principles calculations, Inorg. Chem. 50, 10259 (2011).
- A. Smolyanyuk, L. Šmejkal, and I. I. Mazin, A tool to check whether a symmetrycompensated collinear magnetic material is antiferro- or altermagnetic, SciPost Phys. Codebases 30 (2024).
- I. Mazin and PRX Editors, Altermagnetism a new punch line of fundamental magnetism, Phys. Rev. X 12, 040002 (2022).
- L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
- L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low-z antiferromagnets, Phys. Rev. B 102, 014422 (2020).
- L.-D. Yuan, Z. Wang, J.-W. Luo, and A. Zunger, Prediction of low-z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling, Phys. Rev. Mater. 5, 014409 (2021).
- L. Šmejkal, A. B. Hellenes, R. González-Hernández, J. Sinova, and T. Jungwirth, Giant and tunneling magnetoresistance in unconventional collinear antiferromagnets with nonrelativistic spin-momentum coupling, Phys. Rev. X 12, 011028 (2022).
- R. D. Gonzalez Betancourt, J. Zubáč, R. Gonzalez-Hernandez, K. Geishendorf, Z. Šobáň, G. Springholz, K. Olejník, L. Šmejkal, J. Sinova, T. Jungwirth, et al., Spontaneous anomalous Hall effect arising from an unconventional compensated magnetic phase in a semiconductor, Phys. Rev. Lett. 130, 036702 (2023).
- R. González-Hernández, H. Serrano, and B. Uribe, Spin chern number in altermagnets, Phys. Rev. B 111, 085127 (2025).
- H.-Y. Ma, M. Hu, N. Li, J. Liu, W. Yao, J.-F. Jia, and J. Liu, Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current, Nat. Commun. 12, 2846 (2021).
- G. Grüner, The dynamics of spin-density waves, Rev. Mod. Phys. 66, 1 (1994).
- J. Luttinger, Fermi surface and some simple equilibrium properties of a system of interacting fermions, Phys. Rev. 119, 1153 (1960).
- J. M. Luttinger and J. C. Ward, Ground-state energy of a many-fermion system. II, Phys. Rev. 118, 1417 (1960).
- B. O. Roos, P. R. Taylor, and P. E. Sigbahn, A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach, Chem. Phys. 48, 157 (1980).
- P. E. Siegbahn, J. Almlöf, A. Heiberg, and B. O. Roos, The complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule, J. Chem. Phys. 74, 2384 (1981).
- C. C. J. Roothaan, New developments in molecular orbital theory, Rev. Mod. Phys. 23, 69 (1951).
- K. Andersson, P.-Å. Malmqvist, and B. O. Roos, Second-order perturbation theory with a complete active space self-consistent field reference function, J. Chem. Phys. 96, 1218 (1992).
- S. Wouters and D. Van Neck, The density matrix renormalization group for ab initio quantum chemistry, Eur. Phys. J. D 68, 272 (2014).
- R. J. Bartlett and M. Musiał, Coupled-cluster theory in quantum chemistry, Rev. Mod. Phys. 79, 291 (2007).
- M. Friák, A. Slávik, I. Miháliková, D. Holec, M. Všianská, M. Šob, M. Palm, and J. Neugebauer, Origin of the low magnetic moment in : An ab initio study, Materials 11, 1732 (2018).
- P. Rüßmann, D. Antognini Silva, D. S. G. Bauer, P. Baumeister, P. F. Bornemann, J. Bouaziz, S. Brinker, J. Chico, P. H. Dederichs, B. H. Drittler, et al., JuDFTteam/JuKKR: v3.6, Zenodo (2022), https://zenodo.org/records/7284739.
- E. Di Lucente, F. J. dos Santos, and N. Marzari, Spin fluctuations steer the electronic behavior in the FeSb skutterudite, Materials Cloud Archive 2026.34 (2026).
- R. Guo, X. Wang, and B. Huang, Thermal conductivity of skutterudite from first principles: Substitution and nanoengineering effects, Sci. Rep. 5, 7806 (2015).
- P. V. C. Medeiros, S. Stafström, and J. Björk, Effects of extrinsic and intrinsic perturbations on the electronic structure of graphene: Retaining an effective primitive cell band structure by band unfolding, Phys. Rev. B 89, 041407(R) (2014).
- P. V. C. Medeiros, S. S. Tsirkin, S. Stafström, and J. Björk, Unfolding spinor wave functions and expectation values of general operators: Introducing the unfolding-density operator, Phys. Rev. B 91, 041116(R) (2015).
- M. Iraola, J. L. Mañes, B. Bradlyn, M. K. Horton, T. Neupert, M. G. Vergniory, and S. S. Tsirkin, IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures, Comput. Phys. Commun. 272, 108226 (2022).
- A. J. Cohen, P. Mori-Sánchez, and W. Yang, Insights into current limitations of density functional theory, Science 321, 792 (2008).
- I. Timrov, N. Marzari, and M. Cococcioni, Hp – A code for the calculation of Hubbard parameters using density-functional perturbation theory, Comput. Phys. Commun. 279, 108455 (2022).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- G. Prandini, A. Marrazzo, I. E. Castelli, N. Mounet, and N. Marzari, Precision and efficiency in solid-state pseudopotential calculations, npj Comput. Mater. 4, 72 (2018).
- G. Prandini, A. Marrazzo, I. E. Castelli, N. Mounet, and N. Marzari, A standard solid state pseudopotentials (SSSP) library optimized for precision and efficiency (2020), https://archive.materialscloud.org/record/2018.0001/v4.
- K. Lejaeghere, G. Bihlmayer, T. Björkman, P. Blaha, S. Blügel, V. Blum, D. Caliste, I. E. Castelli, S. J. Clark, A. Dal Corso, et al., Reproducibility in density functional theory calculations of solids, Science 351, aad3000 (2016).
- J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
- A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015).